In the following, we should discuss the mass spectrum of vector bottomonia.
As listed in PDG [1]}, there were
\(\Upsilon (1S)\) , \(\Upsilon (1S)\) , \(\Upsilon (3S)\) , \(\Upsilon (4S)\) , \(\Upsilon (10860)\) , and \(\Upsilon (11020)\) . We find that they form a Regge trajectory
as shown in Fig. REF .
This Regge trajectory satisfies the relation \(M^2=M_0^2+(n-1)\mu ^2\)  [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}. Here, \(M_0\)  is the mass of the ground state, \(M\)  denotes the mass of the radial excitation state with the radial quantum number \(n\) , and \(\mu ^2=7.0403\)  GeV\(^2\)  is the slope of the Regge trajectory.
Although the \(\Upsilon (10753)\)  is suggested as the mixture of \(4S\)  and \(3D\)  states of bottomonium, the \(\Upsilon (10753)\)  has main component of \(3D\)  state. Thus, we may take \(\Upsilon (10753)\)  and the predicted \(\Upsilon (1^3D_1)\)  and \(\Upsilon (2^3D_1)\)   [10]}, [11]}, [12]}, [13]} to construct
another Regge trajectory (see Fig. REF ), which have slope \(\mu ^2=6.3364\)  GeV\(^2\) . This slope is similar to that for the \(S\) -wave bottomonia.
Thus, searching for the missing \(\Upsilon (1^3D_1)\)  and \(\Upsilon (2^3D_1)\)  bottononia in future experiment will be helpful to test this Regge trajectory behavior. It is obvious that the present work of studying the \(\Upsilon (10753)\rightarrow \Upsilon (1^3D_1)\eta \)  shows the potential of finding out the \(\Upsilon (1^3D_1)\)  bottomonium.
